Method for weighing individual micro- and nano-sized particles

ABSTRACT

A method for measuring mass of a micro- and nano-sized particle. The method includes placing the micro- or nano-sized particle on a resonator having an oscillator and a first and second cantilevered arms with interdigitating finger, energizing the oscillator at a selective frequency thereby causing mechanical vibration in the first and second cantilevered arms, directing a light beam from a light source onto the interdigitating fingers, sensing intensity of light of the reflected diffraction pattern by at least one photodetector positioned about at least one of the modes, varying the frequency by sweeping a range of frequencies and correlating the sensed intensity to mass to thereby determine the mass of the micro- or nano-sized particle.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present U.S. patent application is a divisional patent applicationof the U.S. patent application Ser. No. 14/525,155 filed Oct. 27, 2014,which is related to and claims the priority benefit of U.S. ProvisionalPatent Application Ser. No. 61/895,734, filed Oct. 25, 2013, thecontents of each of which is hereby incorporated by reference in itsentirety into the present disclosure.

GOVERNMENT SUPPORT CLAUSE

This invention was made with government support under Grant No. 0925417awarded by the National Science Foundation. The government has certainrights in the invention.

TECHNICAL FIELD

The present application relates to weighting systems and particularly toa micro- and nano-scale weighting system.

BACKGROUND

This section introduces aspects that may help facilitate a betterunderstanding of the disclosure. Accordingly, these statements are to beread in this light and are not to be understood as admissions about whatis or is not prior art.

The need to weigh micro-sized particles has become prevalent. Severalapproaches have been used to accomplish such weighing. One approach isbased on cantilever-based micro/nano-sensors which have been usedextensively over the past decade to detect a wide variety of entitiesincluding bio-molecules, chemicals, viruses and cells. These sensorshave been used both in static (i.e. stress sensing) and dynamic (i.e.resonating) modes. The latter mode reveals the mass of the target entityby measuring changes in the resonance frequency of the cantilever.

Current strategies of weight measurement using cantilevers mostly dependupon probabilistic attachment of the targets on the cantilever surface.For example, resonators have been used to weigh single bacteria andviruses that bind to sensor surfaces both specifically andnonspecifically. The embodiments provided in the prior art have usedsuspended micro-channel resonators to measure bio-molecules and singlenano-particles by flowing the target entities through the innermicro-channel of a cantilever.

The nature of the cantilever-based systems of the prior art, however,render them susceptible to error. Furthermore, the probabilistic natureof target attachment reduces the repeatability of measurements of amicro-particle specimen array. In addition, when one relies onprobabilistic attachment of target entities, this approach makes itchallenging to weigh an individual particle specifically selected by theuser from a pool of other particles whose weights are not desired.

There is, therefore an unmet need for a novel approach to weighindividual micro/nano-sized particles of varying sizes while reducingerrors associated with methodologies used in the prior art.

SUMMARY

A method for measuring mass of a micro- and nano-sized particle isdisclosed. The method includes placing the micro- or nano-sized particleon a resonator. The resonator includes a base portion, an oscillatorcoupled to the base portion configured to vibrate the base portion, afirst cantilevered beam coupled to the base portion at a proximal endand having a tip portion at a distal end, and a second cantilevered beamcoupled to the base portion at a proximal end and having a tip portionat a distal end. Each of the first and second cantilever beams furtherhaving a plurality of fingers near a corresponding tip inwardlypointing, such that the entirety of each cantilever beam forms asubstantially mirror image of the entirety of other. The first pluralityof fingers interdigitating with the second plurality of fingers suchthat the first cantilevered beam and the second cantilevered beam canoscillate independent of each other. The interdigitating fingers areseparated by gaps that are configured to reflect light from theinterdigitating fingers during oscillation of the first and secondcantilevered beams to form a diffraction pattern. The method furtherincludes energizing the oscillator at a selective frequency therebycausing mechanical vibration in the first and second cantilevered arms.Additionally, the method includes directing a light beam from a lightsource onto the interdigitating fingers, sensing intensity of light ofthe reflected diffraction pattern by at least one photodetectorpositioned about at least one of the modes. Furthermore, the methodincludes varying the frequency by sweeping a range of frequencies andcorrelating the sensed intensity to mass to thereby determine the massof the micro- or nano-sized particle.

Another method for measuring mass of a micro- and nano-sized particle isalso disclosed. The method includes placing the micro- or nano-sizedparticle on a resonator, The resonator includes a base portion, anoscillator coupled to the base portion configured to vibrate the baseportion, a first cantilevered beam coupled to the base portion at aproximal end and having a tip portion at a distal end, and a secondcantilevered beam coupled to the base portion at a proximal end andhaving a tip portion at a distal end. Each of the first and secondcantilever beams further having a first plurality of fingers near thefirst tip portion inwardly pointing and a second plurality of fingersnear the second tip portion inwardly pointing, respectively, such thatthe entirety of each cantilever beam is positioned in a side-by-sidemanner next to the entirety of the other. The first plurality of fingersare interdigitating with the second plurality of fingers such that thefirst cantilevered beam and the second cantilevered beam can oscillateindependent of each other. The interdigitating fingers are separated bygaps that are configured to reflect light from the interdigitatingfingers during oscillation of the first and second cantilevered beams toform a diffraction pattern. The method includes energizing theoscillator at a selective frequency thereby causing mechanical vibrationin the first and second cantilevered arms. The method further includesdirecting a light beam from a light source onto the interdigitatingfingers, sensing intensity of light of the reflected diffraction patternby at least one photodetector positioned about at least one of themodes. Furthermore, the method includes varying the frequency bysweeping a range of frequencies, and correlating the sensed intensity tomass to thereby determine the mass of the micro- or nano-sized particle.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other objects, features, and advantages of the presentinvention will become more apparent when taken in conjunction with thefollowing description and drawings wherein identical reference numeralshave been used, where possible, to designate identical features that arecommon to the figures, and wherein:

FIG. 1 is a perspective view of a system for weighing micro- andnano-sized particles incorporating a resonator as described herein.

FIG. 2 is a top view of the resonator of FIG. 1 depicting a plurality ofinterdigitating fingers.

FIG. 2a is an enlarged view of two adjacent interdigitated fingers ofFIG. 2.

FIG. 3 is a graph of frequency shift as a function of the position of atarget particle on a cantilevered arm of the resonator shown in FIG. 1.

FIG. 4 is a graph of frequency differential between an unloadedreference arm and loaded sensor arms of the resonator and system shownin FIG. 1.

FIG. 5 is a graph showing the standard deviation in measured frequencyshift as a function of excitation voltage and loading of the resonatorshown in FIG. 1.

FIG. 6 is a scanning electron micrograph (SEM) of two stem cell spheresmounted on the cantilevered beams of the resonator as shown in FIG. 1.

FIG. 7 is a graph of the frequency spectrum showing the comparativeweighing of the two stem cell spheres depicted in FIG. 6.

FIG. 8 is a micrograph of the resonator of FIG. 1 shown with a sporecluster mounted on the sensor beam and a reference bead mounted on thereference beam, together with an inset view showing an SEM image of thespore cluster.

FIG. 9 is a graph of the change in differential frequency withincreasing humidity for the experimental set-up shown in FIG. 8.

FIG. 10 is an SEM image of the contents of a dried pond water sample.

FIG. 11 is an SEM image of a diatom obtained from the sample shown inFIG. 10, with the diatom mounted on the sensor beam of a resonator asshown in FIG. 1, with an inset of the diatom on the end of the beam.

The attached drawings are for purposes of illustration and are notnecessarily to scale.

DETAILED DESCRIPTION

For the purposes of promoting an understanding of the principles of thepresent disclosure, reference will now be made to the embodimentsillustrated in the drawings, and specific language will be used todescribe the same. It will nevertheless be understood that no limitationof the scope of this disclosure is thereby intended.

The present disclosure describes a system that allows weighing a widevariety of individual micro- and nano-particles by placing them onto aresonator. A single target entity that is selected under a microscope isgrabbed by a micro-manipulator and the entity is placed on the tip of asensor beam of the cantilever for weighing. The particle weight isdetermined using optical diffraction modes, which permits highlyaccurate weight measurements as well as measurement of relative weightdifferences between particles.

In one feature, the system 1 includes a resonator 10, as illustrated inFIGS. 1-2, a light source 30, an optical detector array 40, and afunction generator 52. The light source 30 is configured to shine light32 to the resonator 10. Reflected light 34 reflects from the resonatorand strikes the optical detector array 40 according to a diffractionpattern. The diffraction pattern includes spots or “modes”, including0^(th) mode. The optical detector array 40 includes at least one opticaldetector 36 positioned to sense the intensity of one of the modes, e.g.,the 0^(th) mode.

The resonator 10 includes at least two adjacent beams 12 a, 12 bcantilevered from a base 14. The base 14 is attached to a piezoelectricshaker 50, but can be any electromechanically activated vibrationmechanism. In one use of the resonator 10, one of the beams 12 b servesas an inherent reference operable to suppress noise and otherdisturbances that affect both cantilevers similarly. The other beam 12 aserves as the beam for the target particle. The beams 12 a, 12 b arepreferably identically sized and shaped so that no or only minimaladjustments or calibrations are required to ensure accurate results. Thebeams may be formed in various geometries, but the rectangular geometrydepicted in FIGS. 1-2 may be more suitable for fabrication purposes.Each beam includes a cantilevered arm 16 with the free end defining anenlarged support surface 18 for supporting a target particle. Thesupport surface is enlarged to provide ample area for placement of thetarget particle by a micro-manipulator.

Each beam 12 a and 12 b includes two segments: arms 16 a and 16 b; andsupport surfaces 18 a and 18 b (also referred to as tip portions),respectively. In one important feature, each cantilevered beam includesa plurality of laterally-directed fingers 20 a, 20 b. As seen in thefigures, the fingers are interdigitated so that light illuminating thebeams produces a diffraction pattern, as described herein. The resonatormay be fabricated using known micro-fabrication techniques, such asphotolithography, etching or other known techniques. In the embodimentshown in the figures, the cantilevered beams each have a length of 50 μmto 500 μm or more narrowly between 200 μm to 300 μm; a width at the arms16 a and 16 b of between about 10 μm to 100 μm and a width at thesupport surface 18 of between about 10 μm to 100 μm, or more narrowlybetween 35 μm to 85 μm, not including the interdigitated fingers. Thefingers 20 a, 20 b, depicted in FIG. 2a , each have a width 20 w of 2 to5 μm and a length 20 l of about 10 μm to 100 μm or more narrowly 40 μmto 60 μm and can range between 4 to 15 in number for each set of fingerswith a gap 20 g of 1 μm to 5 μm. The beams 12 a and 12 b each have athickness of about 10 nm to 2 μm, or more narrowly between 500 nm to 1μm.

The resonator may be formed as a silicon-rich silicon nitride layer. Thefingers 20 a and 20 b may be coated with a thin layer of gold to improvereflectivity.

The system 1 includes the light source 30, e.g., a laser (NEWPORTR-30091, 5 mW, for example), that is oriented to illuminate the fingers,as shown in FIG. 1. The photo diode array 40 (THORLABS DET110, forexample) is arranged to measure the intensity of the 0^(th) mode of thereflected diffraction pattern. By analyzing the intensity change of thereflected diffraction mode, the resonance frequencies of bothcantilevers can be deduced. The resonator 10 further includes thepiezoelectric shaker 50 (THORLABS AE0203D04F, for example) that isattached to the bottom of the base 14 for excitation of the resonator.The oscillation amplitude and frequency of the shaker are controlled bya function generator 52 (TEKTRONIX AFG3102, for example). A lock-inamplifier (Stanford Research Systems SR830) is used to record the signalat the excitation frequency.

Changes in resonance frequency are measured to resolve the loading uponthe cantilever, which is expressed by:

$\begin{matrix}{{f = {\frac{1}{2\;\pi}{\sqrt{\frac{K}{{0.243\; M} + m}}\mspace{14mu}\lbrack 19\rbrack}}},} & {{Equation}\mspace{14mu} 1}\end{matrix}$where M is the effective mass of the cantilever,m is the mass of the load, andK is the effective stiffness of the cantilever. Accordingly, thedifference between the resonance frequencies of the reference and thesensor cantilevers are expressed by the following equation:

$\begin{matrix}{{{\Delta\; f} = {\frac{1}{2\;\pi}( {\sqrt{\frac{K}{{0.243\; M} + m_{r}}} - \sqrt{\frac{K}{{0.243\; M} + m}}} )}},} & {{Equation}\mspace{14mu} 2}\end{matrix}$where m_(r) is the added load on the reference cantilever, andm is the added mass on the sensor cantilever. Since the cantilevers arenot perfectly rectangular, K and M can be determined by combining finiteelement simulations with experiments. In one experiment, the effectivedensity of a cantilever beam was taken as 3.65 g/cm³ by averaging a 20nm thick gold layer with a density of 19.3 g/cm³ and a 480 nm ofsilicon-rich silicon nitride layer with a density of 3 g/cm³. TheYoung's modulus was then estimated to be 182.2 GPa by matching theresonance frequency predicted by the finite element simulation with thatobserved experimentally (6642 Hz). Next, the value for K was determinedto be 0.0195 N/m using a finite element simulation by applying avertical point force at the tip and observing the resulting tipdeflection. Finally, M was determined to be 46.08 nano-gram bysubstituting K into the Equation 1. With the constants of the aboveequations determined, the only variables are the masses of the targetand reference particles, m and m_(r).

For maximum measurement sensitivity the load or target is preferablyexactly at the tip of the cantilever. Hence, the micromanipulator herealso serves the purpose of placing the target as close to the tip of thecantilever as possible, improving the accuracy of mass measurements.Nevertheless, the effect of loading location on the resonance frequencycan be addressed in the weight/mass measurement process. An elementanalysis can be used to demonstrate the relationship between theresonance frequency and the location of the center of mass of the targetentity T positioned on the enlarged surface 18 as depicted in FIG. 3.The variation of the resonance frequency shift with different loadingmasses and locations on the sensor arm is demonstrated in the graph ofFIG. 3. The solid line curve corresponds to an empty referencecantilever 12 b and the data points represent the results of the finiteelement simulation for different target entity positions from the freeend or tip of the arm 12 a. For improved accuracy in determining themass, the location of the target entity can be determined usingcalibrated brightfield microscopy and a corresponding frequency shiftvs. mass curve can be generated using finite element analysis.

The graph of FIG. 4 shows experimental results of frequency response ofthe system when one of the cantilevers (the sensor arm 12 a) is loadedwith three different masses. In each experiment, an individualpolystyrene bead (Spherotech) with a different mass was placed on theenlarged surface 18 of the sensor arm 12 a for weighing. Prior to theplacement, the micromanipulator was used to dip the bottom of the beadin a small amount of grease. It has been found that the grease canefficiently improve the adhesion between the target particles and thecantilever surface but has negligible mass (˜70 pico-gram) in comparisonwith the particles being weighed. Alternatively, the grease can beplaced directly on the cantilever surface before placing the targetentities, in which case the impact of the grease on the system frequencyresponse can be directly accounted for before the measurements. In FIG.4, the frequencies corresponding to the two peaks represent theresonance frequencies of the sensor arm 12 a (low frequency peak) andthe reference arm 12 b (high frequency peak). Initially, since bothcantilevers are empty, no significant frequency separation occurs andtwo resonance peaks overlap with each other, as reflected in the lowercurve in the graph of FIG. 4. As the load on the sensor arm increases,the resonance peak corresponding to the sensor arm shifts to the left,while the resonance peak of the reference arm remains fixed, so the tworesonance frequencies separate. The 9.3 nano-gram bead (middle curve)and the 46.5 nano-gram bead (upper curve) were located 11.6 μm and 12.2μm away from the tip of the cantilever, respectively. The resonancefrequency of the reference arm is unchanged because there is nosignificant change of mass on the reference arm.

The mass of the load on the sensor arm can be derived readily from thefrequency separation between the two peaks with a single measurement. Inparticular, the frequency shift value can be applied to Equation 2 tosolve for the value m corresponding to the mass of the target particleT. In the case where no reference mass is added to the referencecantilevered arm 12 b the value for m_(r) is zero. It is furthercontemplated that the system can be used to directly determine thedifferential mass between two particles by loading both cantilevers(instead of leaving the reference arm empty). In this case, thereference arm frequency will also shift to the left in FIG. 4 from theunloaded reference frequency. In Equation 2, the value for m_(r) will benon-zero, corresponding to the mass of the second particle positioned onthe arm 12 b. Alternatively, instead of using the Equations 1 and 2, onecan prefer to determine the added masses by matching the experimentallyobserved resonance frequencies with those observed in a finite elementsimulation of the cantilevered system bearing loads with the same shapeand location as determined microscopically, and varying the value of themasses in simulation until the resulting resonance frequency in thesimulation matches those observed experimentally.

The system shown in FIG. 2, and particularly the resonator 10 shown inFIG. 1, provide repeatable resonance frequency measurements, andconsequently repeatable weight/mass measurements for micro- andnano-particles. In one verification experiment, the sensing cantileverarm 12 a was loaded with an individual polystyrene bead with a knownmass and the peak-to-peak excitation voltage to the piezoelectric shaker50 was varied. Two different beads with different masses (9.3 nano-gramand 46.5 nano-gram) were used and each experiment was repeated fivetimes at each excitation voltage. The standard deviation of the measuredresonance frequency was then calculated. The results shown in the graphof FIG. 5 indicate that the repeatability of the measurements improvesboth with mass loading and with excitation voltage. As reflected in thegraph, increasing the load at each excitation voltage resulted in adecrease in standard deviation, with the decrease being more dramatic atthe higher voltages. As also shown in the graph, as the excitationvoltage is increased the standard deviation decreases for each loadingcondition, with the standard deviation at the highest voltage beingabout one-third the standard deviation at the lowest voltage. Thisreduction in standard deviation is due in part to an increase in massimproving the quality factor of the cantilever, and an increase inexternal excitation improving the signal-to-noise ratio of themeasurement. Hence, in some experiments, in order to reduce the standarddeviation of the measured frequency shift, it may be preferable toprovide a reference bead of known mass on the reference arm 12 b insteadof leaving it unloaded. With this modification, the potential error inthe resonance frequency can be as low as 1 Hz, which corresponds toabout 3 pico-gram with the cantilever mass and stiffness valuesdescribed above (as calculated using Equation 2).

The effect of other uncertainties on the accuracy of the massmeasurement has been investigated. One uncertainty arises from thefabrication of a given wafer forming the resonator 10 may result inwafer dimensions that vary between the two cantilevered arms 12 a, 12B.For instance, in one example a change in thickness due to non-uniformityof nitride deposition was measured as 8 nm over a distance of 3 incheson a photolithography wafer, which for a 500 nm-thick film, could alterthe stiffness of a cantilever by 4.9% (cubic dependence on thickness)and its mass by 1.6% (linear dependence on thickness). According toEquation 1, the combined effect of this stiffness and mass difference onthe natural frequency of a cantilevered arm (with nominal M of 46.08nano-gram and K of 0.0195 N/m) would be about 106 Hz. However, due tothe differential nature of the system as shown in Equation 2, for smallloads up to 2 nano-gram, this effect is suppressed to below 1 Hz Evenfor a 10 nano-gram load, the uncertainty would be only about 11 Hzcorresponding to a potential error of about 100 pico-gram).

In another experiment, two cantilevers that were 2 inches apart on aphotolithography wafer were found to differ in length by as much as 1 μm(possibly due to alignment errors during photolithography). For a 250 μmlong cantilever, the effect of this uncertainty on stiffness can beabout 1.2%, and on mass about 0.4%, with the combined effect producing a53 Hz uncertainty on resonance frequency. However, in a differentialsystem (according to Equation 2) while measuring small loads (<290pico-gram), uncertainty in length results in no detectable error inresonance frequency shift. For a 10 nano-gram load, the uncertaintywould be 19 Hz (about 200 pico-gram). In practice however, these errorscan be mitigated by measuring the dimensions of the particularcantilevers with high accuracy using scanning electron microscopy (SEM)and determining the related M and K before the measurement. For example,a 2 nm uncertainty in measuring thickness in SEM would result in nodetectable errors in measuring loads up to 4.7 nano-gram, a 24 pico-gramerror in measuring a 10 nano-gram load and a 1.5 nano-gram error inmeasuring a 100 nano-gram load. A 2 nm uncertainty in 250 μm nominallength would result in no detectable error in resonance frequency. Notethat the above uncertainty analyses assumed that the referencecantilever is empty. Hence for a differential system, loading thereference cantilever with a mass similar to that on the sensingcantilever can further mitigate the effects of uncertainties. Anotherexperiment evaluated the frequency uncertainty as a function of thelocation of the target particle or load on the cantilevered arms. Ananalysis similar to that shown in the graph of FIG. 3 suggests that a200 nm uncertainty in assessing the location of the load (the limit of atypical brightfield microscope) would result in a 23 pico-gramuncertainty in the measured mass of a 10 nano-gram particle. Thisuncertainty is less than 3 pico-gram while measuring particles thatweigh 1 nano-gram or less. For many applications, this uncertainty canbe further mitigated by measuring the location of the target particle orload using SEM.

Weighing of Individual Stem Cell Spheres

In one procedure, the system was used to weigh individual stem cellspheres. Currently, stem cells are of interest because of their capacityfor organ replenishment and for their potential role in cancerinitiation and progression. Stem cells form multiple spheres in softagar. These spheres are usually not analyzed individually but en masse.With the system disclosed herein an individual stem cell sphere can beextracted from culture medium and weighed. One experiment was conductedwith adolescent male murine prostate stem cell spheres that werecultured for 10 days. The cell spheres were fixed by formalin, followedby dehydration using ethanol. Then, the stem cell spheres were left todry on a glass surface for subsequent testing steps. FIG. 6 illustratesthe SEM image of two stem cell spheres placed on different cantileversfor weighing. One of the cantilevers was loaded with a larger stem cellsphere located 14.2 μm away from the cantilever tip, while the smallersphere was located 9.8 μm away from the cantilever tip. The frequencyresponse of the loaded resonator, as shown in FIG. 7, show a left peakand the right peak of the frequency spectrum illustrate the resonancefrequencies corresponding to the cantilevers loaded with larger andsmaller spheres, respectively. The difference in the masses of both cellspheres is derived from the differential frequency of 1663 Hz as 88.2nano-gram with the mass of the big cell sphere being 114 nano-gram andsmall sphere being 25.8 nano-gram. The ability to easily compare twoindividual stem cell spheres in terms of mass could offer interestingpossibilities in understanding their biology and their response tovarious treatments.

Humidity Response of Bacillus Subtilis Spores

In another procedure the system was used to assess the response ofBacillus subtilis spores to environmental stimuli. These spores canabsorb water, and dehydrate when heated. By weighing the spores atdifferent humidity levels, the amount of water absorbed by the sporescan be measured. The experiment started by collecting spore clustersusing a micromanipulator. After the spores were dried out on a glasssurface, the micromanipulator was employed to tenderly pile up thespores. The multilayered coat structure of each spore renders it as oneof the most durable cell types so that the spores remain intact afterbeing grouped. After collecting sufficient spores, the cluster of sporeswas picked up and placed on the tip of the cantilever arm, which hadbeen pre-paved with a thin layer of grease to prevent the spore clusterfrom flying away. This particular cantilever pair is slightly differentfrom the one used in the previously described experiment hence theeffective stiffness and the effective mass were determined again as0.0187 N/m and 45.6 nano-gram, respectively. As seen in photomicrographof FIG. 8, the sensor arm 12 a of the cantilever resonator was loadedwith a cluster of B. subtilis spores, and the reference arm 12 b wasloaded with a reference bead. The experiment took place in a closedspace to facilitate humidity control.

The resulting relationship between humidity change and mass is shown inthe graph of FIG. 9. The initial frequency shift value is deliberatelyset to 0 for clarity. The initial mass of the spore cluster was 18.8nano-gram, which varied with relative humidity. The mass increased from18.8 nano-gram to 23.2 nano-gram as the relative humidity increased from36% to 92%. The 23.5% increase in the spore mass is in accordance with aprevious study. The effect of humidity on the cantilevers themselves issuppressed by the inherently differential detection. Consequently, onlythe water adsorbed in the spores is measured.

Weighing of Diatoms from Pond Water

In a further example of the versatility of the system and resonatordisclosed herein, the system was used to weigh individual diatom algae.Diatoms are unicellular algae that are widely observed in aquaticenvironments. They have been extensively studied in various fieldsincluding ecology, bioengineering, medicine, and nanotechnology. Due totheir special features (such as amorphous silica skeletons, uniformnano-porous structures, chemical inertness, and versatile forms andsizes) researchers have proposed multiple applications of diatoms suchas in biophotonics, microfluidics, nanofabrication, gel filtration, anddrug delivery, The ability of the system disclosed herein toindividually pick and weigh single diatoms could provide new insightinto their characterization and their use as biotechnological tools. Tomeasure the mass of diatom particles, a cantilever arm with circularhead shape was used to weigh single diatom cells, as shown in the photomicrograph of FIG. 11. The effective stiffness of this particularcantilever pair was 0.0188 N/m and the effective mass was calculated as54.2 nano-gram. In the experiment, a drop of outdoor pond water thatcontained large amounts of diverse microorganisms including bacteria,algae, and protozoa, was first left to dry in air on a glass slide.

FIG. 10 shows a spot on the glass slide with numerous micro-particles, apennate-type diatom and other microorganisms. A single diatom wasextracted using a micromanipulator and place it at the tip of the sensorcantilever for weighing as shown in FIG. 11. A polystyrene bead withknown mass was placed on the reference cantilever arm to improve theresolution of the measurement, as discussed above. The diatom and thereference bead were placed 2.8 μm and 17.4 μm away from the suspendingend of the cantilever, respectively. As a result, the differentialresonance frequency between two adjacent cantilevers was measured as2173 Hz, and the differential mass between the two particles wasmeasured as 42.2 nano-gram with the mass of the diatom being 4.4nano-gram.

In one aspect of the present disclosure, the resonator includes a pairof arms cantilevered from a base, in which the base is configured forengagement with an oscillator or shaker to induce oscillation of thearms. Each arm defines a surface configured to receive a micro- ornano-sized particle or object. The arms further define interdigitatingfingers between each other that are adapted to define a diffractionpattern from incident light reflected from the fingers as thecantilevered arms oscillate. In one method of using the system, a targetparticle is mounted on a sensor arm, while the other arm, or thereference arm, may be unloaded or loaded with a particle having a knownmass. The base of the resonator is oscillated to cause vibration of thecantilevered sensor and reference arms at their respective resonantfrequencies. The resonance frequencies of both aims are obtained bysensing the intensity of a diffraction mode produced by theinterdigitated fingers. This approach prevents the user from having toperform two different experiments (one for each cantilever) and allowsobtaining the two resonance frequencies in one experiment. Hence, thedifferential frequency, or difference between the detected resonantfrequencies of the two arms, is also obtained by the same way. Thedifferential frequency value can be used in an equation to solve for themass of the target particle on the sensor arm. Alternatively, theresonance frequencies observed experimentally can be used in a finiteelement simulation to determine the mass of the loaded particles.

With this versatile method it is possible to isolate fragments of cells,individual cells, or individual groups of cells such as prostate stemcell spheres, from culture and measure their weight. The same system canbe used to aggregate and measure the humidity response of cells, such asspore cells, while minimizing the effect of the humidity on the sensoritself due to the inherently differential nature of the measurement. Thesystem and resonator disclosed herein provides capability of extractingand weighing an individual particle, such as a diatom from a cluster ofmicro-particles found in outdoors pond water.

Those skilled in the art will recognize that numerous modifications canbe made to the specific implementations described above. Theimplementations should not be limited to the particular limitationsdescribed. Other implementations may be possible.

The invention claimed is:
 1. A method for measuring mass of a micro- andnano-sized particle comprising: placing the micro- or nano-sizedparticle on a resonator, the resonator comprising: a base portion, anoscillator coupled to the base portion configured to vibrate the baseportion, a first cantilevered beam coupled to the base portion at aproximal end and having a tip portion at a distal end, and a secondcantilevered beam coupled to the base portion at a proximal end andhaving a tip portion at a distal end, each of the first and secondcantilever beams further having a plurality of fingers near acorresponding tip inwardly pointing, such that the entirety of eachcantilever beam forms a substantially mirror image of the entirety ofother, the first plurality of fingers interdigitating with the secondplurality of fingers such that the first cantilevered beam and thesecond cantilevered beam can oscillate independent of each other, theinterdigitating fingers separated by gaps that are configured to reflectlight from the interdigitating fingers during oscillation of the firstand second cantilevered beams to form a diffraction pattern; energizingthe oscillator at a selective frequency thereby causing mechanicalvibration in the first and second cantilevered arms; directing a lightbeam from a light source onto the interdigitating fingers; sensingintensity of light of a reflected diffraction pattern by at least onephotodetector positioned about at least one of the modes; varying thefrequency by sweeping a range of frequencies; and correlating the sensedintensity to mass to thereby determine the mass of the micro- ornano-sized particle.
 2. The method of claim 1, the energizing furthercomprising: varying the frequency by sweeping a range of frequencies. 3.The method of claim 1, further comprising: determining a resonancefrequency differential between the resonance frequency of each of thecantilevered beams based on the sensed intensity.
 4. The method of claim1, the at least one mode is the 0^(th) mode.
 5. The method of claim 1,the light source is a laser.
 6. The method of claim 1, the first andsecond cantilevered beams are silicon-based.
 7. The method of claim 1,further comprising: placing a reference weight on the resonator, wherethe micro- or nano-sized particle is placed on the first cantileveredbeam and the reference weight is placed on the second cantilevered beam.8. A method for measuring mass of a micro- and nano-sized particlecomprising: placing the micro- or nano-sized particle on a resonator,the resonator comprising: a base portion, an oscillator coupled to thebase portion configured to vibrate the base portion, a firstcantilevered beam coupled to the base portion at a proximal end andhaving a tip portion at a distal end, and a second cantilevered beamcoupled to the base portion at a proximal end and having a tip portionat a distal end, each of the first and second cantilever beams furtherhaving a first plurality of fingers near the first tip portion inwardlypointing and a second plurality of fingers near the second tip portioninwardly pointing, respectively, such that the entirety of eachcantilever beam is positioned in a side-by-side manner next to theentirety of the other, the first plurality of fingers interdigitatingwith the second plurality of fingers such that the first cantileveredbeam and the second cantilevered beam can oscillate independent of eachother, the interdigitating fingers separated by gaps that are configuredto reflect light from the interdigitating fingers during oscillation ofthe first and second cantilevered beams to form a diffraction pattern;energizing the oscillator at a selective frequency thereby causingmechanical vibration in the first and second cantilevered arms;directing a light beam from a light source onto the interdigitatingfingers; sensing intensity of light of the reflected diffraction patternby at least one photodetector positioned about at least one of themodes; varying the frequency by sweeping a range of frequencies; andcorrelating the sensed intensity to mass to thereby determine the massof the micro- or nano-sized particle.
 9. The method of claim 8, theenergizing further comprising: varying the frequency by sweeping a rangeof frequencies.
 10. The method of claim 9, further comprising:determining a resonance frequency differential between the resonancefrequency of each of the cantilevered beams based on the sensedintensity.
 11. The method of claim 8, the at least one mode is the0^(th) mode.
 12. The method of claim 8, the light source is a laser. 13.The method of claim 8, the first and second cantilevered beams aresilicon-based.
 14. The method of claim 8, further comprising: placing areference weight on the resonator, where the micro- or nano-sizedparticle is placed on the first cantilevered beam and the referenceweight is placed on the second cantilevered beam.